The state of the art of detecting low observable aircraft or other targets using radar has not advanced as quickly as the aircrafts themselves and their ability to evade detection. Detection to date had been limited in the type and character of modulation that could be applied to a transmitted signal. For example, the transmitters were incapable of applying arbitrary amplitude and phase modulation. With the advent of linear amplifiers, however, arbitrary amplitude and phase modulation is possible.
The design in U.S. Pat. 5,175,552, issued Dec. 29, 1993, takes advantage of the advances in radar transmission technology by maximizing the S/N ratio of the received echo. A transfer function H.sub.1 (.omega.) is first determined from characteristics that are completely described by the impulse response of the target. Transfer function H.sub.1 (.omega.) of the target is then applied to the transmitted signal s(t) to give y(t), the echo signal directly from the target.
After adding signals representing noise and clutter inherent to the system, a received echo r(t) is modulated by a second transfer function H.sub.2 (.omega.), at the receiver (representative of a receiver), giving us g(t), the finally-received signal. The highest S/N ratio is realized when H.sub.2 (.omega.)=kY*(.omega.), which describes a matched filter in the white noise case. Under this condition, S/N=2E/N.sub.0, so that the S/N ratio is maximized when echo response energy E is maximized.
Energy E is maximized when s(t) is chosen so that EQU E=.intg..vertline.y(.tau.).vertline..sup.2 d.tau. (1)
subject to the constraints EQU s(t)=0 for t .epsilon.[0&lt;t&lt;T]and (2) EQU E.sub.in =.intg.s(.tau.).sup.2 d.tau.&lt;.infin. (3)
Solving by the Calculus of Variations gives EQU s(t)=.mu..intg.s(.tau.).gamma.(t,r)d.tau. (4)
where EQU .gamma.(t,.tau.)=.intg.h.sub.1 (.lambda.-t)h.sub.1 (.lambda.-.tau.)d.lambda.(5)
where h.sub.1 is the impulse response of the target and the Fourier transform of H.sub.1 (.omega.).
Transfer function considerations as just outlined are important in the previous approach--in order to achieve enhanced detection of a response signal from a target. However, it is extremely important to improve upon this prior approach by enhancing the target identification or classification capabilities of a radar signal.